Research On Robust M-estimation Adaptive Filtering Algorithm

The rapid development of modern society puts forward new requirements for signal processing technology.Efficient and convenient signal processing technology often has a broader application prospect.As an important part of modern signal processing technology,adaptive filtering has developed rapidly in recent decades.Although the traditional adaptive filtering algorithm can achieve good convergence performance in the Gaussian environment,for the actual system,the impact noise often occurs,which leads to the degradation of the convergence performance of the adaptive algorithm,and even leads to the serious consequences of the algorithm divergence;the impulse response of the unknown system is usually sparse,and the use of this prior knowledge can significantly improve the adaptive performance When the expected signal of the unknown system is truncated,the traditional adaptive algorithm often has a large deviation.In view of the above problems,this paper improves the existing adaptive algorithms and proposes some robust adaptive algorithms1.Aiming at the problem that the background noise of the sparse system is disturbed by impulsive noise,the M-estimation function is introduced into the reweighted zero attraction least mean square(RZA-LMS)algorithm to realize robust sparse system identification.In order to avoid the trade-off between convergence rate and steady-state error,a robust variable step-size method is derived by using gradient descent method to optimize the performance of the proposed algorithm.To verify the convergence of the proposed algorithm,the mean square convergence is analyzed,and the range of step parameters is obtained,which guides the variable step-size method.2.For the robust identification of sparse systems,the M-estimation function is applied to the convex constrained recursive least squares(CC-RLS)algorithm to achieve faster convergence speed and lower steady-state error.A robust convex constrained recursive minimum M-estimation algorithm(R3LM)is derived.By analyzing the selection of rule function and law factor,better convergence performance is achieved.For different sparse systems,the convergence performance of the proposed algorithm is different by choosing different sparse constraints.R3 lm leaves a large choice for the design of the algorithm.3.From the perspective of probability theory,a probabilistic regression model is used to model the censored system.The LMM algorithm is used to identify the parameters of the model,and the variable step-size method is used to optimize the performance of the proposed algorithm.Then the mean convergence and mean square convergence of the proposed algorithm are analyzed to obtain the necessary and sufficient conditions for the stability of the algorithm,and the theoretical results of mean square deviation are derived.Through the simulation experiment of MATLAB software,the performance superiority of several adaptive system identification algorithms proposed in this paper is proved.